Fastest way to turn a ring of unconnected vertices into an edgeloop?
Select all the inner faces with Circle Select or Lasso tool. Press F to create a face, then X and Only Faces to remove the face and leave just the edges. Select the outer vertices and repeat FX. You should now have two loops - simply select all and Bridge Edge Loops.

As an alternative to Bridge Edge Loops, select two adjacent pairs of vertices and remove the two edges between each and join opposite ones to make a ‘C’ shape that almost joins. Select all and Grid Fill. Select the vertices around the gap and F to create the face.

Animated gif showing the process :